Locomotion Control of a Biped Robot Using Nonlinear Oscillators

Recently, many experiments and analyses with biped robots have been carried out. Steady walking of a biped robot implies a stable limit cycle in the state space of the robot. In the design of a locomotion control system, there are primarily three problems associated with achieving such a stable limit cycle: the design of the motion of each limb, interlimb coordination, and posture control. In addition to these problems, when environmental conditions change or disturbances are added to the robot, there is the added problem of obtaining robust walking against them. In this paper we attempt to solve these problems and propose a locomotion control system for a biped robot to achieve robust walking by the robot using nonlinear oscillators, each of which has a stable limit cycle. The nominal trajectories of each limb's joints are designed by the phases of the oscillators, and the interlimb coordination is designed by the phase relation between the oscillators. The phases of the oscillators are reset and the nominal trajectories are modified using sensory feedbacks that depend on the posture and motion of the robot to achieve stable and robust walking. We verify the effectiveness of the proposed locomotion control system, analyzing the dynamic properties of the walking motion by numerical simulations and hardware experiments. Shinya Aoi received the B.E. and M.E. degrees from the Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan in 2001 and 2003, respectively. He is a Ph.D. candidate in the Department of Aeronautics and Astronautics, Kyoto University. Since 2003, he has been a research fellow of the Japan Society for the Promotion of Science (JSPS). His research interests include dynamics and control of robotic systems, especially legged robots. He is a member of IEEE, SICE, and RSJ. Kazuo Tsuchiya received the B.S., M.S., and Ph.D. degrees in engineering from Kyoto University, Kyoto, Japan in 1966, 1968, and 1975, respectively. From 1968 to 1990, he was a research member of Central Research Laboratory in Mitsubishi Electric Corporation, Amagasaki, Japan. From 1990 to 1995, he was a professor at the Department of Computer Controlled Machinery, Osaka University, Osaka, Japan. Since 1995, he has been a professor at the Department of Aeronautics and Astronautics, Kyoto University. His fields of research include dynamic analysis, guidance, and control of space vehicles, and nonlinear system theory for distributed autonomous systems. He is currently the principal investigator of “Research and Education on Complex Functional Mechanical Systems” under the 21st Century Center of Excellence Program (COE program of the Ministry of Education, Culture, Sports, Science and Technology, Japan).     

Adaptive Robot Biped Locomotion with Dynamic Motion Primitives and Coupled Phase Oscillators

In order to properly function in real-world environments, the gait of a humanoid robot must be able to adapt to new situations as well as to deal with unexpected perturbations. A promising research direction is the modular generation of movements that results from the combination of a set of basic primitives. In this paper, we present a robot control framework that provides adaptive biped locomotion by combining the modulation of dynamic movement primitives (DMPs) with rhythm and phase coordination. The first objective is to explore the use of rhythmic movement primitives for generating biped locomotion from human demonstrations. The second objective is to evaluate how the proposed framework can be used to generalize and adapt the human demonstrations by adjusting a few open control parameters of the learned model. This paper contributes with a particular view into the problem of adaptive locomotion by addressing three aspects that, in the specific context of biped robots, have not received much attention. First, the demonstrations examples are extracted from human gaits in which the human stance foot will be constrained to remain in flat contact with the ground, forcing the “bent-knee” at all times in contrast with the typical straight-legged style. Second, this paper addresses the important concept of generalization from a single demonstration. Third, a clear departure is assumed from the classical control that forces the robot’s motion to follow a predefined fixed timing into a more event-based controller. The applicability of the proposed control architecture is demonstrated by numerical simulations, focusing on the adaptation of the robot’s gait pattern to irregularities on the ground surface, stepping over obstacles and, at the same time, on the tolerance to external disturbances.     

Robot Dynamic Modeling Using a Power Flow Approach with Application to Biped Locomotion

In this paper, we present a method for robots modeling called bidirectional dynamic modeling. This new method takes into account the gear efficiency and the direction of power transmission in the gears. Epicyclic gearboxes have often different efficiencies in the two directions of power transmission. The characteristics of the chain of transmission must then be taken into consideration in order to describe the dynamic behavior of robots. The two directions of power flow can indeed occur in robot motions. Depending on that direction the dynamic model is different. The bidirectional dynamic modeling is experimentally applied to a bipedal walking robot. Our method exhibits a better accuracy over classical modeling. Moreover, when applied to computed torque control, the bidirectional model increases the tracking performances.     

基于Webots的蛇形机器人翻滚运动仿真及实现

针对蛇形机器人的侧向翻滚运动,给出一种建立正交关节蛇形机器人三维空间运动模型的方法,提出了一种更为简单的实现蛇形机器人侧向翻滚运动的舵机输入函数.通过选择不同的控制参数,可以实现蛇形机器人"U"字形和"V"字形侧向翻滚运动.在Webots移动机器人仿真软件上进行正交关节蛇形机器人翻滚运动仿真,并在蛇形机器人本体上进行试验,验证了所提控制规律的有效性.     

小型双足步行机器人的机构设计及其运动仿真

小型双足步行机器人具有多关节、多驱动器、多自由度的特点,本文以人体全身17个主要关节及其运动特性为研究对象,利用三维设计软件CATIA设计出小型双足步行机器人的全身机构,根据ZMP理论,以正常人行走的“X”形交叉动作为原则,规划出其各关节转角,在ADAMS下对其虚拟样机进行运动仿真,确保实现机器人的稳定步行和做舞蹈动作。     

Design and Modeling of a Snake Robot Based on Worm-Like Locomotion

In this paper we restrict our attention to worm-like, vertical traveling wave locomotion and present detailed kinematics and dynamics of a planar multi-link snake robot. Lagrange's method is used to obtain the robot dynamics. Webots software is used for simulation and to experimentally investigate the effects of link shape on motor torques. Using the dynamics model and Webots simulation, a nine-link snake robot is designed and constructed. Physical experiments are carried out to validate the mathematical model. Webots software is also used to perform simulation and further validate theoretical results. Finally, stability of the snake robot is experimentally investigated.     

双足机器人的两种步态规划的解耦分析及比较

在双足机器人行走步态规划的研究中,首先对前进方向和侧面摆动进行解耦,建立运动学数学模型,运用ZMP稳定性判据作为双足机器人行走稳定性判断标准,利用时序构造函数法和三次样条插值法对双足机器人运行步态进行规划。利用matlab软件编程和仿真,能够体现出不同规划方法下步行状态在时间和空间的特征,仿真结果对比表明,利用三次样条插值法的步态规划,能够更好的反映出双足机器人的步行稳定性。     

双足机器人跨越动态障碍物在线控制系统设计

在双足机器人跨越动态障碍物的在线控制问题中,脚步规划和步态控制的学习时间是关键问题;提出了一种将机器人的步态控制和脚步规划分别独立设计的控制策略;步态控制目的是产生关节点轨迹并控制对理想轨迹的跟踪,考虑到双足机器人关节点轨迹的不连续性,应用小脑模型连接控制CMAC记忆特征步态的关节点轨迹;脚步规划的控制目标是通过对环境的视觉感知预测机器人的运动路径,算法是基于无需对动态环境精确建模的模糊Q学习算法;仿真结果表明该控制策略的可行性,并且可以有效缩短在线学习时间。     

双足步行机器人的步态规划

主要研究了双足步行机器人的基本步态的建立过程,进行了参数化处理,提出了一种简单可行的步态规划方法,并对数据结果进行了仿真验证。仿真及试验结果表明,该文给出的方法能实现不同步速的连续动态步行。通过标准步态数据的建立,为实时步态规划校正和在线控制补偿算法奠定了基础。     

Error Analysis and Effective Adjustment of the Walking-Ready Posture for a Biped Humanoid Robot

A walking control algorithm is generally a mixture of various controllers; it depends on the characteristics of the target system. Simply adopting one part of another researcher's algorithm does not guarantee an improvement in walking performance. However, this paper proposes an effective algorithm that can be easily adopted to other biped humanoid robots; the algorithm enhances the walking performance and stability of the robot merely by adjusting the walking-ready posture. The walking performance of biped humanoid robots is easily affected by an unsuitable walking-ready posture in terms of accuracy and repeatability. More specifically, low accuracy for the walking-ready posture may cause a large difference between an actual biped robot and its mathematical model, and the low repeatability may disturb the evaluation of the performances of balance controllers. Therefore, this paper first discusses the factors that detrimentally affect bipedal walking performance and their phenomena in the walking-ready posture. The necessary conditions for an ideal walking-ready posture are then defined based on static equilibrium and a suitable adjustment algorithm is proposed. Finally, the effectiveness of the algorithm is verified through dynamic computer simulations.     

双足机器人运动学三维仿真研究

机器人三维图形仿真是机器人离线控制系统开发中的重要环节.为优化机器人的位姿,双足机器人由于具有多自由度、强耦合和高度非线性等特点,其运动学仿真研究大都集中在各个关节的运动学二维曲线上,很难有三维可视化运动效果.针对这一难点,对双足机器人提出了一种树形数据结构.通过采用结构并结合机器人连杆机构的运动学原理,设计了一种机器人运动的矩阵变换方法.根据上述方法,树形Matlab平台可视化编程实现了双足机器人运动学三维仿真,并作了仿真双足机器人的行走动作和进行动作优化.为实物机器人的研制提供了可靠的技术依据.     

基于遗传算法的双足步行机器人步行姿态控制策略

本文基于ZMP理论、位姿矩阵及遗传算法,在已经使用刚体数学建模的机器人上实现机器人步态控制。首先我们使用ZMP步态控制理论,对机器人的步态稳定性进行分析,采用了遗传算法对参数的选择,实现机器人的步态控制.     

Energy-Efficient and High-Speed Dynamic Biped Locomotion Based on Principle of Parametric Excitation

We clarified that the common necessary condition for generating a dynamic gait results from the requirement to restore mechanical energy through studies on passive dynamic walking mechanisms. This paper proposes a novel method of generating a dynamic gait that can be found in the mechanism of a swing inspired by the principle of parametric excitation using telescopic leg actuation. We first introduce a simple underactuated biped model with telescopic legs and semicircular feet and propose a law to control the telescopic leg motion. We found that a high-speed dynamic bipedal gait can easily be generated by only pumping the swing leg mass. We then conducted parametric studies by adjusting the control and physical parameters and determined how well the basic gait performed by introducing some performance indexes. Improvements in energy efficiency by using an elastic-element effect were also numerically investigated. Further, we theoretically proved that semicircular feet have a mechanism that decreases the energy dissipated by heel-strike collisions. We provide insights throughout this paper into how zero-moment-point-free robots can generate a novel biped gait.      

基于ADAMS的双足机器人建模与仿真

为了提高双足机器人的设计效率,可以通过虚拟样机技术对其进行设计与仿真。针对机器人设计双足行走步态,首先以实际的物理样机为原型,建立双足机器人的七连杆模型,并用解析法求得机器人的逆运动学模型;然后在ADAMS软件中建立参数化的虚拟样机模型,在Matlab软件中规划双足机器人在平地上的完整行走步态;最后将规划的步态导入ADAMS中,在虚拟样机上实现了双足机器人的行走仿真。仿真结果与规划的行走步态基本一致,验证了虚拟样机的有效性,从而为双足机器人的设计与步态规划提供了一种新的方法和可靠依据。     

基于控制函数的蛇形机器人攀爬运动分析

为实现对正交关节蛇形机器人多种运动形式的简单、统一控制,从研究蛇形机器人控制函数出发,提出了一种简单的并可同时实现正交关节蛇形机器人蜿蜒运动、行波运动、侧向翻滚运动和螺旋攀爬运动等多种运动形式的控制函数.对蛇形机器人实现螺旋攀爬运动的控制参数进行了分析,并用粒子群优化算法(PSO)对控制参数进行了优化拟合,给出了控制参...     

Analysis of Creeping Locomotion of a Snake-like Robot on a Slope

The diverse locomotion modes and physiology of biological snakes make them supremely adapted for their environment. To model the noteworthy features of these snakes we have developed a snake-like robot that has no forward direction driving force. In order to enhance the ability of our robot to adapt to the environment, in this study we investigate the creeping locomotion of a snake-like robot on a slope. A computer simulator is presented for analysis of the creeping locomotion of the snake-like robot on a slope, and the environmentally-adaptable body shape for our robot is also derived through this simulator.     

Robust Sliding-mode Control of Nine-link Biped Robot Walking

A nine-link planar biped robot model is considered which, in addition tothe main links (i.e., legs, thighs and trunk), includes a two-segment foot.First, a continuous walking pattern of the biped on a flat terrain issynthesized, and the corresponding desired trajectories of the robot jointsare calculated. Next, the kinematic and dynamic equations that describe itslocomotion during the various walking phases are briefly presented. Finally,a nonlinear robust control approach is followed, motivated by the fact thatthe control which has to guarantee the stability of the biped robot musttake into account its exact nonlinear dynamics. However, an accurate modelof the biped robot is not available in practice, due to the existence ofuncertainties of various kinds such as unmodeled dynamics and parameterinaccuracies. Therefore, under the assumption that the estimation error onthe unknown (probably time-varying) parameters is bounded by a givenfunction, a sliding-mode controller is applied, which provides a successfulway to preserve stability and achieve good performance, despite the presenceof strong modeling imprecisions or uncertainties. The paper includes a setof representative simulation results that demonstrate the very good behaviorof the sliding-mode robust biped controller.     

Development of Biped Robot MARI-3 for Jumping

A biped robot, MARI-3, for jumping is developed, of which the ultimate objective is fast walking and running. Its mechanical structure including the joint configuration and specification, the knee joint, and the speed reduction mechanism are described in detail. A specific control system RON (RObot Network) for MARI-3 that is a serial and distributed network and consists of a microcontroller, host unit, servo units, sensor units and servo amplifiers is presented as well as the sensor system. With the developed biped robot MARI-3, one-leg jumping of 110 ms jumping time and 4.0 cm jumping height was implemented as initiative and verification experiments. Furthermore, by comparison of MARI-3 with other jumping or running robots, MARI-3's potential ability for fast walking, jumping and running becomes clear.     

Robust Recurrent Neural Network Control of Biped Robot

In this paper, a recurrent neural network (RNN) control scheme is proposed for a biped robot trajectory tracking system. An adaptive online training algorithm is optimized to improve the transient response of the network via so-called conic sector theorem. Furthermore, L ₂-stability of weight estimation error of RNN is guaranteed such that the robustness of the controller is ensured in the presence of uncertainties. In consideration of practical applications, the algorithm is developed in the discrete-time domain. Simulations for a seven-link robot model are presented to justify the advantage of the proposed approach. We give comparisons between the standard PD control and the proposed RNN compensation method.     

双足机器人上楼梯步态的规划与控制

研究双足机器人上楼路径优化技术,为了让双足机器人实现稳定的上楼梯的行走,应规划双足机器人的上楼梯的步态.为解决对步态进行合理规划与稳定控制问题,提出用几何约束法,用摆线拟合踝关节运动轨迹,设计模糊控制器,对踝关节的滚转角度进行调整,使ZMP位置靠近支撑区域中心,保证了机器人的稳定行走;最后在ADAMS软件中建立了双足机器人的虚拟样机,并通过与Matlab的联合仿真,实现了双足机器人上楼梯的稳定行走仿真.仿真结果验证了上楼梯步态与模糊控制器的有效性,为系统设计提供了保证.